Melt the butter in a saucepan over low heat; add the garlic and cook for 30 seconds.
Add 3/4 cup of the stock and the tomatoes.
Bring to a boil.
Reduce the heat and simmer, uncovered, over medium heat for about 10 minutes or until the tomatoes are tender.
Add the cream and bring to a boil, stirring.
Simmer over medium heat until the sauce is thick enough to coat the back of a spoon.
(The sauce can be kept, covered, for 1 day in the refrigerator. Heat again over low heat.)
Sprinkle the chicken with salt and pepper on both sides.
Heat the oil in a large, heavy skillet over medium-high heat.
Add the chicken and saute, pressing on the chicken occasionally with a slotted spatula, for about 4 minutes per side or until the meat feels springy and is no longer pink inside (cut to check).
Transfer to a board; cover and keep warm.
Discard the fat from the skillet.
Add the remaining stock and bring to a boil, stirring up the pan juices.
Boil to reduce slightly, then add to the sauce.
Stir in the basil.
Taste and adjust the seasoning.
Meanwhile, cook the pasta, uncovered, in a large port of boiling salted water over high heat, stirring occasionally (about 1 to 2 minutes for fresh or 3 to 5 minutes for dried fettucine), or until tender but firm to the bite (al dente).
Drain, transfer to bowl and toss with 3 or 4 tablespoons of the sauce.
Cut each chicken breasts into 2 or 3 diagonal slices.
Reheat gently in the sauce if needed.
Transfer the pasta to serving plates, top with the chicken and coat with sauce.